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The magic of flight

December 23 -- North Pole -- Toy production in Santa's workshop was halted early today by Chief Elf Bernie Noel, who called an emergency meeting of the sleigh committee. "Gentlemen, we have a serious problem," Noel warned. "It appears we may not have enough reindeer power to lift the sleigh on Christmas Eve, thus jeopardizing the delivery of toys to good little girls and boys." "Yes, Santa has certainly put on a few extra pounds," said Senior Sleigh Project Elf Chris Carol. "According to my preliminary investigation, eight tiny reindeer just won't cut it. Since Rudolph channels his energy into his red nose to light the way, I don't think we can count on him to help pull the weight. We may need to add a couple of the backup reindeer." While the elves engage in small group discussion, let's ask an SwRI Whizard to lend a hand with the calculations.

"Have you ever wondered why those C-5 Galaxies don't fall out of the sky? Well, so have I! The answer lies in the fact that air is actually quite dense and sticky. We don't think of it that way because we move at very slow speeds most of the time, but when you move faster and faster, you find out that the air gets harder and harder to move against. If you double your speed, you hit twice as many molecules of air during a given time, and you hit them twice as hard, so the force required increases as the square of the speed. Now if we could just harness that force and make it push up, we could use it to oppose gravity. We do that with a device called a wing.

"Wing lift is a function of surface area, velocity through the air, and the density of the air. Since Santa's sleigh is a fixed size and we can't do much about the density of the air, we'll have to work on the velocity. Lift increases as the square of the speed, but so does drag -- the force you feel when you try to walk into a strong wind. So to lift a heftier Santa, we'll need more power to overcome the added drag at a higher speed. The bad news is that the power requirement increases as the third power of the speed, what we call a cubic function. So, if Santa weighs 10 percent more than last year, we'll need a 15.4 percent increase in power to get the sleigh off the ground. We had a nine-reindeer hitch last year (Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and of course, Rudolph, but Rudolph doesn't pull much.) So, we need about 1.23 additional reindeer. Hmmm.

"Way back in 1977, Dr. Paul MacCready won the Kremer prize for man-powered flight (named for British industrialist Henry Kremer). He did it by analyzing the power equation, which says the power required equals the drag-to-lift ratio times the weight to the two-thirds power, divided by the wing span. Human power is limited to about one-third horsepower, so most folks that tried to win the prize tried to optimize the length-to-diameter ratio. MacCready looked at the exponent on the weight term and concluded that small weight savings would yield big power savings. He won the $50,000 prize! And you thought algebra wasn't useful for anything! (By his own admission, his major objective wasn't to get into the record book -- he just needed the money!)

"So let's see. In order to fly, we can increase power by adding reindeer, increase the wing span by modifying the sleigh, or get rid of some excess weight. Santa gained 10 percent. He's easily 300 pounds, so we need to get rid of 30 pounds so he can get back below maximum takeoff weight with the existing power. He's only got one day to diet, so that won't work. I know! Since he carries that bag of coal to put into the stockings of all the bad little boys and girls, we'll just omit the coal this year! Voila! Airborne again! It's like magic! Merry Christmas to all, and to all a good night!"

Thanks to this month's Whizard, Dave Musgrave, former manager of the product design section in the Space Science and Engineering Division. An amateur pilot since 1991, Musgrave aviates in a Cessna 172 whenever he gets a spare moment.

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February 27, 2014